1. Field of the Invention
This invention relates to a detector head for obtaining scale signals from a measuring device using a magnetic or optical scaling device and, more particularly, to improvements in removing distortion in the scaling detector signals and for improving the precision of the measuring device.
2. Description of the Prior Art
As is known, there are measurement systems of various types, such as magnetic, optical, magnetic induction, and capacitance. All of these systems detect variations in magnetic flux, optical intensity, induced voltage, or electrostatic capacitance, corresponding to some displacement and transform the variations into electric signals by using a reference scale having a periodically varying pattern and a pickup head that undergoes the displacement.
In order to increase the resolving power, the detector output of these systems is often divided into a plurality of portions that are much smaller than the period of the pattern in the reference scale, so that precise positions of the pickup head can be obtained by the electrical division, that is, by interpolation. For this purpose, it is desirable that the waveform of the detector output be approximately sinusoidal, with distortion of the waveform being kept at a minimum. In the case where the waveform of the detector output is distorted, even if the electrical division (interpolation) is possible, high precision measurements cannot be obtained. Moreover, in the optical or capacitance kinds of systems, because the waveform of the detector output, which corresponds to variations in optical intensity or capacitance, is trapezoidal or triangular with respect to the mechanical displacement, it contains harmonic components, principally third order harmonic components.
This trapezoidal waveform can be represented by: ##EQU1## and the triangular waveform by: ##EQU2## The distortion factor can be calculated by using the following formula: ##EQU3## Thus, it can be seen that the major part of the distortion that is present can be attributed to third order harmonic components.
The above-described situation exists for a magnetic head, for example, in a phase-modulation type scaling device, in which a magnetic grating on a magnetic scale is read out by a multiple-gap head responsive to magnetic flux, as disclosed in Japanese provisional publication No. 137812/82. In such scaling device, scaling signals detected by a conventional multiple-gap head responsive to magnetic flux contain third order harmonic components in addition to the fundamental components, and this gives rise to the above-described drawbacks because interpolation errors are provoked by distortions due to these third order harmonic components. The present invention is based upon a study of the causes of these errors.
In order to improve the resolving power of a precision measuring system or a machine tool using the above-described scaling device, it is necessary to electrically interpolate for a distance equal to the pitch of the grating, however, for various reasons, in the course of this interpolation, interpolation errors are produced. The principal reasons are variations in the distance between the heads of the individual channels, direct current deviations in the reproduction output signal levels, variations in the amplitudes of the reproduced output signals, and distortions due to the third order harmonic components in the reproduction output.
In order to realize a high precision measurement, the interpolation errors should be suppressed and all errors, except for those due to the third order harmonic components, can be alleviated by electrical regulation. Distortion due to third order harmonic components are provoked in the electro-magnetic transformation system by various causes, such as noise in the electrical circuit and scale distortions, to name only a few, but the errors due to scale distortions are the most important. Consequently, interpolation errors can be reduced significantly by removing these scale distortions.
The interpolation errors due to third-order harmonic components can be calculated as follows. Supposing that the third order harmonic wave is C.sub.3 times as large as the fundamental wave, then the output voltage e of a head can be represented by: ##EQU4##
By assuming that .omega.ot=T and ##EQU5## the following equation can be obtained: ##EQU6## Assuming that C.sub.3 =0, equation (6) above can be simplified to: EQU e=sin (T-X) (7)
Consequently, when T=X, e=0, that is, X can be obtained by detecting the phase difference between the voltage represented by equation (7) and the reference wave e=sin T.
Putting T=X+.DELTA.X, equation (6) can be transformed to: EQU e=sin (X+.DELTA.X) {cos X+C.sub.3 cos 3X}-cos (X+.DELTA.X) {sin X-C.sub.3 sin 3X} (8)
Assuming that e=0, .DELTA.X remains an interpolation error and can be calculated as follows: ##EQU7##